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The average score of a batsman in 11 innings is 70. The average score in 10 innings is 64. If S is the score in his 11th inning, then which of the following is/are correct?

A. S/2 > 64

B. S < 110

C. 64 < S < 70

D. 200 < 2S < 300 
1. Only A
2. B and C
3. A and D
4. B and D

1 Answer

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Best answer
Correct Answer - Option 3 : A and D

Given:

Average score in 11 innings = 70

Average score in 10 innings = 64

Formula Used:

Average = Sum of values/Number of values

Calculation:

Sum of score in 10 innings = Average score in 10 innings × Number of innings

⇒ Sum of score in 10 innings = 64 × 10

⇒ Sum of score in 10 innings = 640

Sum of score in 11 innings = Average score in 11 innings × Number of innings

⇒ Sum of score in 11 innings = 70 × 11

⇒ Sum of score in 11 innings = 770

Sum of score in 10 innings + Score in 11th inning = 770

⇒ 640 + S = 770

⇒ S = 130

Checking options:

A. S/2 > 64

130/2 = 65

⇒ 65 > 64

⇒ A is correct.

B. S < 110

130 > 110

⇒ B is not correct.

C. 64 < S < 70

130 > 70

⇒ C is not correct

D. 200 < 2S < 300

2S = 260

⇒ 200 < 260 < 300

⇒ D is correct.

A and D are correct

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